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## Standard Form

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**How to say big numbers!**Starter What could each of these numbers represent? How do you even say them? Why might they be annoying to use? • 37,200,000,000,000 • Estimate for the number of cells in the human body “Thirty-seven trillion, two hundred billion” b) 38,000,000,000,000,000m • Rough distance to Alpha Centauri in metres (third nearest star to Earth) “Thirty-eight quadrillion” c) 1,989,000,000,000,000,000,000,000,000,000kg • Estimated weight of the sun in kilograms “One nonillion, nine hundred and eighty-nine octillion”**Standard Form**• You may have seen Standard Form in Science • It is a way of writing very big or very small numbers a bit more easily • For example 38,000,000,000,000,000m This is the distance from Earth to Alpha Centauri 0.000000000000144m The width of a some molecules**Standard Form**Standard Form numbers are written as a number between 1 and 10 (not including 10), multiplied by a power of 10 Let’s the number 5000 as an example: 5000 = 5000 x 1 = 5000 x 100 Using powers of 10 = 500 x 10 = 500 x 101 This is 5000 in Standard Form as the first number is between 1 and 10! = 50 x 100 = 50 x 102 = 5 x 1000 = 5 x 103 = 0.5 x 10000 = 0.5 x 104 = 0.05 x 100000 = 0.05 x 105**Standard Form**Standard Form numbers are written as a number between 1 and 10 (not including 10), multiplied by a power of 10 Let’s the number 46300 as an example: 46300 = 46300 x 1 = 46300 x 100 Using powers of 10 = 4630 x 10 = 4630 x 101 = 463 x 100 = 463 x 102 This is 46300 in Standard Form as the first number is between 1 and 10! = 46.3 x 1000 = 46.3 x 103 = 4.63 x 10000 = 4.63 x 104 = 0.463 x 100000 = 0.463 x 105**Standard Form**• The distance from Earth to the Moon is: 3.8 x 105 km Write this in full: So the answer in full is 380,000km 3 8 0 0 0 0**Standard Form**• The Empire state building weighs approximately: 3.65 x 108 kilograms Write this in full: So the answer in full is 365,000,000kg 3 6 5 0 0 0 0 0 0**Standard Form**• Write in Standard Form: 23,400,000,000m Write this in full: The decimal has to ‘move’ 10 places to make the first number between 1 and 10 2.34 x 1010 2 3 4 0 0 0 0 0 0 0 0**Standard Form**• You also need to be able to deal with Standard Form with very small numbers! • What might these represent? • 0.000000003m • The width of a DNA strand (3 nanometres) b) 0.00000000028m The size of a water molecule (280 picometres)**Standard Form**Standard Form numbers are written as a number between 1 and 10 (not including 10), multiplied by a power of 10 Let’s the number 0.0007 as an example: 0.0007 = 0.0007 ÷ 1 = 0.0007 ÷ 100 = 0.0007 x 100 Write as multiplications ÷ 103 = x 10-3 = 0.007 ÷ 10 = 0.007 ÷ 101 = 0.007 x 10-1 Using powers of 10 = 0.07 ÷ 100 = 0.07 ÷ 102 = 0.07 x 10-2 = 0.7 ÷ 1000 = 0.7 ÷ 103 = 0.7 x 10-3 = 7 ÷ 10000 = 7 ÷ 104 = 7 x 10-4 = 70 ÷ 100000 = 70 ÷ 105 = 70 x 10-5 This is 0.0007 in Standard Form as the first number is between 1 and 10!**Standard Form**• Write as a decimal number; 8 x 10-4 0.0008 0 0 0 0 8**Standard Form**• Write as a decimal number; 6.51 x 10-8 0.0000000651 0 0 0 0 0 0 0 0 6 5 1**Standard Form**• Write as Standard Form; 0.000073 7.3 x 10-5 0 0 0 0 0 7 3**Plenary**The scale of the universe – a big range of Standard Form numbers!**Summary**• We have learnt what Standard Form is, and where it is used • We have learnt how to write Standard Form numbers as ordinary ‘decimal’ numbers • We have seen an awesome webpage of the very big and the very small!